Zur Idealtheorie von Segal-Algebren

Abstract

It is known that for every Segal algebra S¹(G) in L¹(G) with right approximate units there is a bijective correspondence between the closed right ideals of S¹(G) and those of L¹(G) ([3], §9, Theorem 1). For abelian groups H. Reiter showed that under this correspondence also the existence of approximate units is preserved ([3], §16, Theorem 1). Here among similar results a very simple proof of this fact is given for right approximate units in two-sided ideals which works without the assumption that G be abelian. In fact, the result can be established for abstract Segal algebras, in the sense of J. Burnham [1].